A071558 Smallest k such that n*k + 1 and n*k - 1 are twin primes.

4, 2, 2, 1, 6, 1, 6, 9, 2, 3, 18, 1, 24, 3, 2, 12, 6, 1, 12, 3, 2, 9, 6, 3, 6, 12, 4, 15, 12, 1, 42, 6, 6, 3, 12, 2, 54, 6, 8, 6, 30, 1, 24, 15, 4, 3, 6, 4, 18, 3, 2, 6, 120, 2, 12, 48, 4, 6, 18, 1, 258, 21, 14, 3, 30, 3, 24, 15, 2, 6, 18, 1, 84, 27, 2, 3, 6, 4, 132, 3, 10, 15, 54, 5, 12, 12

Offset: 1

Author

Benoit Cloitre, May 30 2002

Keywords

• easy
• nonn
• changed

Comments

Conjecture: a(n) < sqrt(n)*log(n) for all n > 17261. This has been verified for n up to 3*10^7. It implies the inequality a(n) < n for each n > 127. - Zhi-Wei Sun, Jan 07 2013

A200996(n) <= a(n). - Reinhard Zumkeller, Feb 14 2013

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Crossrefs

Cf. A071256, A001097, A086686, A034693.

Cf. A071407 (k at prime n).

Cf. A220143, A220144 (record values).

Programs

Haskell

a071558 n = head [k | k <- [1..], let x = k * n,
                      a010051' (x - 1) == 1, a010051' (x + 1) == 1]
-- Reinhard Zumkeller, Feb 14 2013

Mathematica

Table[k=1; While[!And@@PrimeQ[n*k+{1,-1}],k++]; k,{n,86}] (* Jayanta Basu, May 26 2013 *)

PARI

a(n) = my(s=1); while(isprime(s*n+1)*isprime(n*s-1)==0, s++); s;